In the zero knowledge protocol discussed in class Alice registers with Victor two isomorphic graphs G1 and G2 and keeps the isomorphism π between them secret. Whenever Victor needs to verify that Alice knows the isomorphism between G1 and G1 they perform n rounds of the following protocol:Alice creates a graph H isomorphic to G1 and G2 and send is to VictorVictor flips a coin and asks Alice either (i) to show that H and G1 are isomorphic, or (ii) to show that H and G2 are isomorphic.Alice sends Victor the requested isomorphism.Assume now that Alice knows a vertex cover S of size k for a large graph G. Alice registers the graph G with Victor and the size k of the vertex cover, but she keep the vertex cover S secret. Design a zero knowledge protocol that Alice and Victor can use to prove that Alice knows a vertex cover of size k for G.(Hint. In each round Alice creates a graph H isomorphic to G. What questions does Victor ask Alice?)

Dear Student, The zero knowledge protocol along with explanation is given below -

Answered: discussed in class Alice registers with…

Computer Networking: A Top-Down Approach (7th Edition)

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In the zero knowledge protocol discussed in class Alice registers with Victor two isomorphic graphs G1 and G2 and keeps the isomorphism π between them secret. Whenever Victor needs to verify that Alice knows the isomorphism between G1 and G1 they perform n rounds of the following protocol:

Alice creates a graph H isomorphic to G1 and G2 and send is to Victor
Victor flips a coin and asks Alice either (i) to show that H and G1 are isomorphic, or (ii) to show that H and G2 are isomorphic.
Alice sends Victor the requested isomorphism.

Assume now that Alice knows a vertex cover S of size k for a large graph G. Alice registers the graph G with Victor and the size k of the vertex cover, but she keep the vertex cover S secret. Design a zero knowledge protocol that Alice and Victor can use to prove that Alice knows a vertex cover of size k for G.

(Hint. In each round Alice creates a graph H isomorphic to G. What questions does Victor ask Alice?)

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